Personalised medicine, digital innovations, and neuro-technologies all offer significant potential benefit for human health and welfare, but also raise complex governance challenges. A variety of approaches have been adopted in the governance of innovative medicines and health technologies, including risk assessment, ethics and self-governance. Recently anticipatory or ‘upstream’ modes of governance have garnered favour. Anticipatory regulation demands a closer relationship between regulators and innovators, to shape the trajectories of the technology. In the EU context, responsible research and innovation has emerged as a key mechanism of governance. This is linked but distinct from a human rights governance which has the advantage of exerting both legal and moral force. What is needed in the healthcare context are governance models which ensure human rights considerations are taken into account from the earliest stages of innovation, to maximise the likelihood that developments are from the outset beneficial and oriented towards protecting ethical values.